有限循环群中与序列的index相关的零和问题研究
发布时间：2018-12-26 11:31
【摘要】：零和理论是组合数论的重要组成部分,其主要研究有限Abe1加法群中序列的组合性质.而与序列的index相关的零和问题又是近几年来零和领域研究的热点.零和序列是零和问题研究的主要对象.与零和序列相关的组合常数的确定问题被称为直接零和问题;与之对应的极值序列,如零和自由序列与n-零和自由序列结构刻画是零和问题的反问题.本文从反零和问题的角度,考虑n阶循环群Cn上与序列的index相关的零和问题.本文工作主要有以下几个方面:1.介绍零和问题的研究背景以及对序列index相关零和问题研究的进展;说明本文中常用符号的含义;阐述加性数论以及群论的相关定理和一些基本概念;以及给出本文的结构安排.2.综述有限循环群Cn上与最小零和序列相关的组合常数l(Cn)的确定以及零和序列和零和自由序列结构刻画问题.考虑了长度大于(n+2)/3的零和自由序列S的结构特点.3.总结循环群Cn上的n-零和自由序列的结构刻画问题.基于长度大于(3n)/2-1的n-零和自由序列的结构刻画,结合前人的工作,本文对长度大于(4n)/3-1的n-零和自由序列的结构的部分情况进行刻画.
[Abstract]:The theory of zero sum is an important part of combinatorial number theory. It mainly studies the combinatorial properties of sequences in finite Abe1 additive groups. The zero sum problem related to the index of sequences is a hot topic in the field of zero sum in recent years. Zero sum sequence is the main research object of zero sum problem. The problem of determining combinatorial constants related to zero-sum sequences is called direct zero-sum problem, and the corresponding extremal sequences, such as zero-sum free sequences and nzero-sum free sequences structure characterization is the inverse problem of zero-sum problem. In this paper, from the point of view of anti-zero sum problem, we consider the zero-sum problem related to the index of sequences on the n-order cyclic group Cn. The main work of this paper is as follows: 1. This paper introduces the research background of zero-sum problem and the research progress of sequence index correlation zero-sum problem, explains the meaning of common symbols in this paper, expounds the related theorems and some basic concepts of additive number theory and group theory. And give the structure of this paper. 2. This paper reviews the determination of the combination constant l (Cn) related to the minimum zero-sum sequence on the finite cyclic group Cn and the characterization of the zero-sum sequence and the zero-sum free sequence structure. The structural characteristics of zero sum free sequence S with length greater than (N2) / 3 are considered. The structure characterization of n- zero sum free sequences on cyclic group Cn is summarized. Based on the structural characterization of nzero-sum free sequences with length greater than (3n) / 2-1 and previous work, this paper describes some cases of nzero-sum free sequences with length greater than (4n) / 3-1.
【学位授予单位】：大连海事大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O156
本文编号：2392066
[Abstract]:The theory of zero sum is an important part of combinatorial number theory. It mainly studies the combinatorial properties of sequences in finite Abe1 additive groups. The zero sum problem related to the index of sequences is a hot topic in the field of zero sum in recent years. Zero sum sequence is the main research object of zero sum problem. The problem of determining combinatorial constants related to zero-sum sequences is called direct zero-sum problem, and the corresponding extremal sequences, such as zero-sum free sequences and nzero-sum free sequences structure characterization is the inverse problem of zero-sum problem. In this paper, from the point of view of anti-zero sum problem, we consider the zero-sum problem related to the index of sequences on the n-order cyclic group Cn. The main work of this paper is as follows: 1. This paper introduces the research background of zero-sum problem and the research progress of sequence index correlation zero-sum problem, explains the meaning of common symbols in this paper, expounds the related theorems and some basic concepts of additive number theory and group theory. And give the structure of this paper. 2. This paper reviews the determination of the combination constant l (Cn) related to the minimum zero-sum sequence on the finite cyclic group Cn and the characterization of the zero-sum sequence and the zero-sum free sequence structure. The structural characteristics of zero sum free sequence S with length greater than (N2) / 3 are considered. The structure characterization of n- zero sum free sequences on cyclic group Cn is summarized. Based on the structural characterization of nzero-sum free sequences with length greater than (3n) / 2-1 and previous work, this paper describes some cases of nzero-sum free sequences with length greater than (4n) / 3-1.
【学位授予单位】：大连海事大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O156
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